- Title
- Gravity wave interaction with an articulated submerged plate resting on a Winkler foundation
- Creator
- Boral, S.; Sahoo, T.; Meylan, M. H.
- Relation
- Applied Mathematical Modelling Vol. 113, Issue January 2023, p. 416-438
- Publisher Link
- http://dx.doi.org/10.1016/j.apm.2022.09.007
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2023
- Description
- Surface gravity wave interaction with an articulated flexible submerged plate in the presence of lateral compressive force is investigated within the framework of blocking dynamics, assuming that the submerged plate is resting on a uniform Winkler foundation. The problem is studied considering small-amplitude plate response and linearised water wave theory in finite water depth. The loci of the dispersion relation reveal the occurrence of wave blocking in the submerged plate mode for a range of wave frequency and compressive force when the submerged plate is resting on a Winker foundation. However, in the absence of the Winkler foundation, no wave blocking occurs in the plate mode irrespective of the values of compressive force, and plane wave propagation in plate mode does not happen for particular values of compressive force. Four propagating wavenumbers exist within the blocking frequencies, of which one is in the surface mode, and others are in the submerged plate mode. Thus, to account for the four propagating wave modes, the existing solution approach for a pair of propagating wave modes is modified in an appropriate manner within the limit of blocking frequencies. Consequently, the energy relation is obtained using Green’s identity, in which the reflection and transmission coefficients are a combination of the amplitudes of different reflected and transmitted wave modes and the associated energy transfer rates. The reflection coefficient in the submerged plate mode jumps from one to zero for very small values of frequency due to the introduction of the Winkler foundation in the presence of compressive force. In addition, zero wave reflection occurs for a higher frequency range with an increase in the values of the Winkler constant. Removable discontinuities are observed at the blocking and saddle points, whilst jump discontinuities occur in the reflection and transmission coefficients due to the change of incident wave mode within the blocking frequencies. Linear time-dependent displacements in surface and submerged plate modes are presented prior to the blocking limit.
- Subject
- submerged articulated plate; wave blocking; wave scattering; energy balance relation; reflection and transmission coefficients; time domain simulation
- Identifier
- http://hdl.handle.net/1959.13/1478758
- Identifier
- uon:50221
- Identifier
- ISSN:0307-904X
- Language
- eng
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